Problem: You are given an unweighted tree with n vertices. Recall that a tree is a connected undirected graph without cycles.

Your task is to choose three distinct vertices a, b, c on this tree such that the number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c is the maximum possible. See the notes section for a better understanding.

The simple path is the path that visits each vertex at most once.

Input

The first line contains one integer number n (3 ≤ n ≤ 2 ⋅ 10^5) — the number of vertices in the tree. 

Next n - 1 lines describe the edges of the tree in form a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i). It is guaranteed that given graph is a tree.

Output

In the first line print one integer res — the maximum number of edges which belong to at least one of the simple paths between a and b, b and c, or a and c.

In the second line print three integers a, b, c such that 1 ≤ a, b, c ≤ n and a ≠, b ≠ c, a ≠ c.

If there are several answers, you can print any.

Example

Input


8
1 2
2 3
3 4
4 5
4 6
3 7
3 8


Output


5
1 8 6

Note

The picture corresponding to the first example (and another one correct answer):

<image>

If you choose vertices 1, 5, 6 then the path between 1 and 5 consists of edges (1, 2), (2, 3), (3, 4), (4, 5), the path between 1 and 6 consists of edges (1, 2), (2, 3), (3, 4), (4, 6) and the path between 5 and 6 consists of edges (4, 5), (4, 6). The union of these paths is (1, 2), (2, 3), (3, 4), (4, 5), (4, 6) so the answer is 5. It can be shown that there is no better answer.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public class Main {
    InputReader in;
    final long mod=1000000007;
    StringBuilder sb;
    public static void main(String[] args) throws java.lang.Exception {
        new Main().run();
    }
    void run() throws Exception {
        in=new InputReader(System.in);
        sb = new  StringBuilder();        
        int t=1;
        for(int i=1;i<=t;i++)
            solve();
        System.out.print(sb);
    }
    ArrayList<Integer> adj[];
    int dis[], p[];
    void dfs(int v, int par) {
        p[v]=par;
        dis[v]=dis[par]+1;
        for(Integer x : adj[v]) {
            if(x!=par)
                dfs(x, v);
        }   
    }
    void solve() {
        int i, j;
        int n=i();
        adj=new ArrayList[n+1];
        dis=new int[n+1];
        p=new int[n+1];
        dis[0]=-1;
        for(i=0;i<=n;i++)
            adj[i]=new ArrayList<>();
        for(i=1;i<n;i++) {
            int x=i(), y=i();
            adj[x].add(y);
            adj[y].add(x);
        }
        dfs(1, 0);
        int max=0, a=0, b=0;
        for(i=2;i<=n;i++) {
            if(dis[i]>max) {
                max=dis[i];
                a=i;
            }
        }
        dfs(a, 0);
        int ans=0;
        for(i=1;i<=n;i++) {
            if(ans<dis[i])  {
                ans=dis[i];
                b=i;
            }
        }
        ArrayList<Integer> diam = new ArrayList<>();
        while(b!=a) {
            diam.add(b);
            b=p[b];
        }
        diam.add(a);
        if(diam.size()==n) {
            sb.append((n-1)+"\n");
            sb.append(diam.get(0)+" "+diam.get(1)+" "+a+"\n");
            return;
        }
        boolean vis[]=new boolean[n+1];
        LinkedList<Integer> queue = new LinkedList<>();
        for(i=0;i<diam.size();i++) {
            queue.add(diam.get(i));
            vis[diam.get(i)]=true;
        }
        dis=new int[n+1];
        while(queue.size()!=0) {
            int v=queue.poll();
            for(Integer u : adj[v]) {
                if(!vis[u]) {
                    queue.add(u);
                    dis[u]=dis[v]+1;
                    vis[u]=true;
                }
            }
        }
        max=0;
        int pos=0;
        for(i=1;i<=n;i++) {
            if(max<dis[i]) {
                max=dis[i];
                pos=i;
            }
        }
        sb.append((diam.size()+max-1)+"\n");
        sb.append(diam.get(0)+" "+pos+" "+a+"\n");
    }
    long mul(long x, long y) {long ans = x*y;return (ans>=mod ? ans%mod : ans);}
    long power(long x, long y, long p) {  
        long res = 1;       
        x = x % p;  
        if (x == 0) return 0;   
        while (y > 0) {
            if((y & 1)==1) 
                res = (res * x) % p;  
            y = y >> 1;  
            x = (x * x) % p;  
        } 
        return res%p; 
    } 
    long gcd(long a, long b) { return (b==0)?a:gcd(b,a%b); }
    int gcd(int a, int b) { return (b==0)?a:gcd(b,a%b); }
    String s() { return in.next(); }
    int i() { return in.nextInt(); }
    long l() {return in.nextLong();}
    class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        public InputReader(InputStream stream) {
            this.stream = stream;
        }
        public int read() {
            if (numChars == -1)
                throw new UnknownError();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new UnknownError();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public int peek() {
            if (numChars == -1)
                return -1;
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    return -1;
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar];
        }
        public void skip(int x) {
            while (x-->0)
                read();
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public String nextString() {
            return next();
        }
        public String next() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
 
            return res.toString();
        }
        public String nextLine() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                if (c != '\r')
                    buf.appendCodePoint(c);
                c = read();
            }
            return buf.toString();
        }
        public double nextDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        public boolean hasNext() {
            int value;
            while (isSpaceChar(value = peek()) && value != -1)
                read();
            return value != -1;
        }
        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}